Analytic Functions With Conic Domains Associated With Certain Generalized q-integral Operator

Abstract

In this paper, we define a new subclass of k-uniformly starlike functions of order-gamma (0 <= gamma < 1) by using certain generalized q integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q sufficient coefficient condition, q-Fekete-Szego inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order-gamma by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.